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Question

The equation y2exy=9e−3.x2 defines y as a differentiable function of x. The value of dydx for x=−1 and y=3 is

A
152
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B
95
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C
3
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D
15
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Solution

The correct option is D 15
y2exy=9e3.x2
Differentiate both sides
ddx(y2exy)=ddx(9e3x2)
2ydydxexy+y2exy(xdydx+y)=9e3(2x)
On solving, we get
dydx=18xe3y3exy2yexy+y2exyx
putting x=1,y=3, we get
dydx=18e327e36e39e3=45e33e3=15

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